Every email account in the world has 2 services that complete the email communication process:

1.  The incoming account service where the email is retrieved to the email client (e.g. Outlook, Firefox, Outlook Express, etc)

2.  The Outgoing account service that packages the email and delivers it to the worldwide web.  This service is referred to as the SMTP (Simple Mail Transfer Protocol).

Your EBSuite account is, of course, web based and if you use an email account within the application you need to consider and maybe adjust the email services that send and receive email in the account.  The incoming setting are, of course, exclusively setup by the email account owner.  The outgoing settings can be shared, but you cannot assume it will be done for you.

The EBSuite account offers 2 places to setup the SMTP (outgoing) server:

1.  The account setting:  Admin > Organization Profile > Outbound Email Settings.  This is used exclusively for System email messages - not as a default SMTP for users.

2.  Within each and every individual user, the user may setup their own SMTP (and incoming account) settings.

 
The individual user NEVER uses the default SMTP setting of the main account (scenario 1.).

If the individual user  DOES NOT setup their own SMTP the outgoing email will use:  mail.ebsuite.com (the EBSuite default SMTP which is publicly available). 

The consideraton with the default (mail.ebsuite.com) is not that it won't work, because it will.  But, the outgoing mail will have a mismatch between the SMTP domain name and the individual user's domain name.  Consequently, some recipients will not receive their email because that looks like SPAM because of the mismatch of domain names.